It has become desirable to maximize the open air or open roof space above the passenger compartment, and it is common in the automotive industry to employ a convertible roof which is movable from a closed position above a passenger compartment to a retracted position. It is also known to provide movable tonneau covers to cover the stowed convertible roof. By way of example, a known convertible system can include a displaceable roof that can be opened as a whole in relation to its opening. The displaceable roof can include a sunroof that can be displaced in relation to a surrounding roof part when the roof is in the closed position. With this known system, it is possible to directly open the roof from closed position when the sunroof is open as well as from a closed position when the sunroof is closed. Another traditional vehicle convertible system employs a flexible fabric roof which can be closed by manually snapping or otherwise attaching the fabric roof to stationary roof rails and a front header. This fabric roof can also be manually rolled up to expose fully the passenger compartment between the roof rails.